I was thinking about the graphs of different trig functions and noticed that most of them are of a similar shape to some different types of polynomials. For example:
- Higher degree polynomials create a wave like sin or cos
- $x^3$ looks like one repetition of tan, and could be flipped and shifted to look like cot
- Each repetition of sec and csc looks like two quadratic parabolas
While obviously the polynomials aren't going to be an exact approximation, are there a set of coefficients that create a reasonably close (to a few decimal places) approximation of one period of the trig functions?
If so, is this useful? Or are there other, better, post Pre Calculus approximations of the trig functions?
Seems to me that you are getting ready for Taylor series of trig functions. I would suggest to google this and you are getting lots of answers
http://en.wikipedia.org/wiki/Taylor_series would do but there are many many other great sites.
As far as usefullness, that can't be even described in one sentence. I appreciate you being inquisitive. That approach is very good, therefore (+1)